Question

In a triangle PQR, PQ=QR, A and B are the mid-points of `bar(QR)` and `bar(PR)` respectively. A circle passes through P,Q, A and B. Then which of the following is necessarily true?
A. `triangle` is equilateral
B. `triangle` is right isosceles
C. PQ is a diameter
D. Both a) and c)

Answer 1

Correct Answer - D
i) Draw the figure and mark the point on it.
ii) Join BQ, now BQ is the median to PR. Since PQ=QR, BQ is also the altitude to PR.
iii) PBQ is a right triangle, right angled at B. Thus, PQ is the diameter.
iv) Joining PA, we get another right triangle PAQ which is right angled at A. PBQ and PAQ are congruent angles.
iv) PR=QR, so `trianglePQR` is an equilateral triangle.